Abstract

The brain is a complex system whose function relies on a diverse set of connections or interactions between brain regions.
Using the mathematical framework of complex networks, these interaction patterns can be parsimoniously represented as brain
graphs: each brain area is represented as a network node and each connection is represented as a network edge. These methods
have been used to demonstrate that human brain networks display properties such as a small‐world architecture that may directly
facilitate cognitive processes. Moreover, mounting evidence suggests that these properties are altered in disease states,
potentially providing important biomarkers for psychiatric and neurological disorders and informing our understanding of the
mechanisms of altered cognitive function. Here, the basic concepts in network science are reviewed, and the properties of
healthy and diseased brain networks discussed. Relationships between network diagnostics and alterations in behavioural or
cognitive variables associated with Alzheimer's disease, schizophrenia and epilepsy are highlighted.

Key Concepts

The brain is a complex system that can be represented by a graph.

In a graph, nodes represent brain regions and edges represent the links or connections between those areas, forming a complex
network.

Brain networks display properties such as a small‐world architecture or a hierarchical modular organisation that may directly
facilitate cognitive processes.

These properties are altered in disease states, potentially providing important biomarkers for psychiatric and neurological
disorders.

Figure 3. Epileptic Functional Networks: ECoG sensors placed on the surface of the brain record local brain dynamics. Functional networks are then created over different periods of time to study the evolution of the epileptic network.

Achard S et al. (2012) Hubs of brain functional networks are radically reorganized in comatose patients. Proceedings of the National Academy of Sciences of the United States of America 109 (50): 20608–20613.

Sporns O (2011) Networks of the Brain. Cambridge, MA: MIT press. (This book by Olaf Sporns provides an extended introduction to and summary of the field of network neuroscience. Of immediate use to practicing neuroscientists, it is also highly accessible to undergraduate readers.)